Room-Temperature Skyrmion Thermopower in Fe3Sn2

We present first room-temperature thermoelectric signature of the skyrmion lattice. This was observed in Fe3Sn2, a Kagome Dirac crystal with massive Dirac fermions that features high-temperature skyrmion phase. The room-temperature skyrmion lattice shows magnetic-field dependence of the wavevector whereas thermopower is dominated by the electronic diffusion mechanism, allowing for the skyrmionic bubble lattice detection. Our results pave the way for the future skyrmion-based devices based on the manipulation of the thermal gradient.


Introduction
Strong electronic correlations and topology are widely recognized as fundamental sources of novel states of matter [1]- [5] and technologically important material properties. [6], [7] Nanoscale magnetic skyrmions in spin textures of chiral magnets are quintessential embodiment of this concept. [8], [9] Magnetic skyrmions are commonly observed by microscopy techniques in the real space and neutron scattering in the reciprocal space. [10], [11] Experiments available far below room temperature reveal no discernible [12] or relatively small changes [13] in magnetic-field dependent thermoelectric properties in the course of transition to the skyrmion crystal.
In magnetic metals thermopower includes electronic diffusion, phonon or magnon-drag thermopower. [14] Thermoelectric signature of the skyrmion lattice, in particular, is of interest in spintronics and spincaloritronics for information processing. [15], [16] Ferromagnetic Fe3Sn2 with a geometrically frustrated kagome bilayer of Fe attracts considerable interest due to its magnetic structure, anomalous Hall effect (AHE), Dirac electronic states and room-temperature skyrmion lattice. [17]- [21] Previous studies also show that skyrmion lattice in Fe3Sn2 can be manipulated by spatially geometric confinement. [22] Moreover, single-chain skyrmion bubbles in 600 nm nanostripes were reported to be stable far above the room temperature, up to 630 K, thus making significant progress towards nanoscale skyrmion -based spintronic. [23] On the other hand, it is also of interest to manipulate skyrmionic textures by thermal gradients in magnetic nanodevices. [24]- [26] In this paper we show first evidence of the room-temperature skyrmion detection by thermopower in Fe3Sn2 and discuss relevant mechanism.

Results
The powder XRD pattern of Fe3Sn2 shows that all observed peaks can be well fitted with the R-3mh space group [ Fig. 1(a)] confirming high purity of the single crystals. The determined lattice parameters a = b =5.345(2) Å and c =19.780(2) Å are in good agreement with the reported values. [27] In the single-crystal XRD [ Fig. 1(b)], only (00l) peaks are detected, indicating that the crystal surface is parallel to the hexagoal plane and orthogonal to the c axis. In Fig. 2 holographically reconstructed magnetization map shows hexagonally packed skyrmionic bubble lattice at the room temperature. [19] Interestingly, the helicity (in-plane spin rotation sense) is either clockwise or anticlockwise, yielding +1 and -1, respectively, as topological charges.
We performed real-space imaging of magnetic spin structures in the ab plane and their evolution under external magnetic field along the c-axis in transmission electron microscope at room temperature and we also also show the magnetic-field-dependent thermopower (S) in the wellestablished skyrmionic bubble phase [19] (Fig. 3). The Lorentz contrasts of skyrmionic bubbles [ Fig. 3(a-d)] are similar to the previous Lorentz microscopy study. [19] We mapped out the projected in-plane magnetization by off-axis electron holography under the residual magnetic field (11.7 mT) at room temperature. In order to stabilize the skyrmionic bubbles at 11.7 mT, a large external magnetic field ~ 1000 mT was abruptly turned off. Under the residual magnetic field (~ 11.7 mT with the objective lense fully off) in our microscope, Lorentz microscopy image [ Fig. 3(a)] shows coexistence of stripes and bubbles in the ab plane. The hexagonally packed skyrmionic bubble lattices are induced in external magnetic field in the range of 600 mT ~ 800 mT [ Fig. 3(b-d)], corresponding to the magnetic field range where the anomaly is observed in the measurements of room-temperature thermoelectric power and heat capacity [ Fig. 3(e,f)]. In addition, we note that the skyrmionic bubble lattice were completely annihilated with magnetic field above 1 T [19] , which is consistent not only with the thermopower [ Fig. 3
From the data presented above it is clear that magnetic skyrmions, topologically protected nanoscale spin textures [28] , show clear signature in room-temperature macroscopic thermal measurements. In what follows we discuss relevant microscopic mechanim. We first note that in µ0H = 9 T applied along the c-axis, changes in resistivity ρ(T), thermal conductivity κ and thermopower S are subtle [ Fig. 4(a,b)]. Metallic ρ(T) argues in favor of considerable electronic diffusion S(T) but the phonon-drag mechanism should also be considered. Thermopower changes from negative to positive at 124(1) K in the absence of magnetic field on cooling, however the sign change moves to 129(1) K and 130(1) K when 9 T is applied in the hexagonal (ab) plane and along the c-axis, respectively. As shown by the red dash dot line in the Fig. 4(b), thermopower shows linear dependence on temperature above 124 K consistent with electronic diffusion. In metallic materials with substantial carrier density Lorentz force will affect thermal and electrical transport alike, whereas dominant carriers are often either electrons or holes. [29], [30] When the magnetic field is applied along the c-axis, resistivity is either unchanged or somewhat decreased above about 120 K and shows positive magnetoresistance (MR) below 120 K whereas there is a up to 20% decrease in κ(9 T) when compared to the κ(0 T) below 100 K, suggesting that electronic contribution to thermal conductivity is not negligible. × 10 -2 J/molK 2 . The phonon velocity is ~2010 ms -1 . [31] Both electron and phonon part of heat capacity are calculated up to the room temperature and are also shown in Figure 4(c).
Next, we evaluate phonon drag vs. electronic diffusion mechanism on thermopower. The characteristic peak in thermal conductivity observed on cooling [ Fig. 4

(a)] is phonon-related
and it commonly arises due to competition between the point-defect/boundary scattering and the Umklapp phonon scattering mechanism. [32] Possible phonon drag effects are supported by the sign change of S(T) at 124 K [ Fig. 4(b)]. If we take change in the band structure and effective mass of Fe3Sn2 into consideration, the low-temperature sign change can not be [33]- [35] As a qualitative estimation, if Drude's formula = 2 * is adopted for the conductivity σ where n is carrier concentration, m* is effective mass and τ is relaxation time inversely proportional to the density of states, then the energy dependencies from the charge carrier density and τ are approximately balanced out, i.e. σ has the same energy dependence as 1/m*. For Fe3Sn2, around the Fermi energy the effective mass decreases. [21] This means σ will increase with energy and yield the negative sign of S. Consequently contributions from other scattering processes such as phonon-drag or magnon-drag must be taken into consideration. Fermi surface of Fe3Sn2 features two dominant electron pockets. [20], [21] Negative thermopower should be expected if the electronic diffusion part Sd in S = Sd + Sp prevails over phonon-drag contribution Sp. This is indeed observed above 124 (K) and is in agreement with a decrease in the absolute values of the temperature-dependent thermopower in 9 T when compared to the S(0 T) [ Fig. 4(b)]. As we show below, electronic diffusion mechanism can explain the linear change of S with temperature above 124fK, but not the positive thermopower at lower temperatures.
In order to study the sign change, we plot only measured S(T) below 124 K [ Fig. 4(d) . [36] By linear fitting the data above 124 K [ Fig. 4(b)] and extrapolating it down to 2 K, we obtain the diffusive part of thermopower at low temperature. The fitted value of EF is 0.25 (1) Fig. 4(c)], phonon velocity and MFP of the phonon, respectively. The results are shown in the inset of Fig. 4(d). Whereas phonon-drag mechanism is commonly associated with much longer mean-free path, we note that phonon drag in metals may not vary significantly with mean free path if energies of electron and phonon distributions are well matched, i.e. if the probability of electron interaction with quasi-balistic phonons is proportional to the size of the region where phonons propagate without mutual collisions. [38], [39] The presence of phonon contribution to thermopower explains the magnetic-field induced changes at low temperature. The absolute value of Sd decreases in 9 T due to the Lorentz force whereas the Sp remains unchanged. Since Sd and Sp have the opposite sign and at low temperature Sp dominates, the net thermopower will increase. This explains the increase of thermopower crossover temperature from 124 K to 129 K for magnetic field in the hexagonal plane or 130 K when the magnetic field is applied along the easy magnetization caxis.

Discussion
The above discussion confirms that, whereas phonon or magnon drag contribute to lowtemperature thermopower, electronic diffusion mechanism is dominant at the room-temperature.
In Fig. 3 (e) the magnetic field is applied along the c-axis and perpendicular to the thermal current flow, so that the thermal transport is measured in the plane of the skyrmionic lattice.
When a thermal gradient ∇ is applied, a diffusion electric current density Jd is generated. The diffusion part of thermopower Sd is the ratio between the electric field required to stop Jd and the ∇ . [40] When a conduction electron transverses a skyrmion, it is affected by the local magnetization and hence continuously changes direction acquiring Berry phase. [41], [42] Consequently, carriers experience effective Lorentz force which increases the Hall effect.
Similar effects should take place when carriers are driven by external thermal gradient. [15] Indeed, as shown in Fig.3(e), thermopower shows well-defined anomaly in the skyrmionic bubble phase. This is in contrast to thermopower outside the skyrmion region, such as for example in the spin glass state at 50 K. When electronic system enters skyrmion region, there is an increase in the absolute values of S(B). For systems with spin degree of freedom, the entropy is composed by the entropy from spin and crystal lattice. Ordering spin texture in skyrmionic phase will decrease the spin entropy and transfer it to the crystal lattice. [43] This part of entropy gives extra driving force to the thermal diffusion of conduction electrons, which will enhance the thermopower as magnetic stripe domains are gradually transformed into bubbles with increasing Zeeman field. [19] Further increase in magnetic field up to 9 T generates additional negative effect on thermopower from the spontaneous magnetization that exceeds the contributions from the entropy, resulting in a decrease in S as skyrmion bubble spin textures die out in higher magnetic fields. It also should be noted that magnetic-field dependent heat capacity [ Fig. 3(f)] shows small, but discernible changes at room temperature. The oscillation amplitudes are up to about 2%, comparable to thermopower-related oscillations at 28 K in MnSi, and are absent outside (H,T) skyrmion region [ Fig. 3(e)]. Since both thermopower S and heat capacity C show magnetic field-induced anomalies where skyrmions form, [19] this also may suggest that thermopower variations stem from topological quantum oscillations induced by DOS changes [44] where Zeeman field increase in skyrmion crystal induces DOS oscillations that arise from the magnetic-field dependence of the wavevector Q and directly affect electronic thermopower from the Mott formula relation. [44] Interestingly, two independent sets of triple-q systems under 585.1 mT were observed in our Lorentz microscopy, as shown in Fig. 3(c). With further increasing magnetic field to 727.5 mT [ Fig. 3(d)

Summary and conclusion
In summary, we present first signature of room-temperature skyrmion spin textures by thermopower. Therrmal transport in the high-temperature region is governed by electronic diffusion mechanism, enabling detection of topologically protected skyrmionic spin textures.
Our results open new possibilities for skyrmion manipulation in future information storage and spin caloritronic devices using thermal gradients. [45], [46] Experimental Section

Crystal synthesis
Single crystals of Fe3Sn2 were grown using flux method. [47] Whereas some crystals were initially grown by mixing Fe and Sn in 5:95 stoichiometry, heating to 1150 ˚C, holding at this temperature for 24 hours, fast-cooling to 910 ˚C and then slow cooling to 800 ˚C [48] , cooling to 770 ˚C was used to to increase the size of crystal to about 3 mm length. [20] Characterization Crystal structure was determined by analyzing powder

Electrical and thermal transport measurements
Resistivity, heat capacity and thermal transport (TTO) properties were measured in a Quantum Design PPMS-9. Standard four contact method was used to measure transport properties.
Electrical resistivity (ρ) was measured for the current ow in the hexagonal plane and the magnetic field (H) was applied along the c axis whereas thermal conductivity (κ) and thermopower S measurements were taken for the heat flow along the ab plane and magnetic field applied both in the hexagonal plane and along the c axis of the crystallographic unit cell. [48] W. Ren, and C. Petrovic (unpublished).  Color-contour composite image obtained from the magnetic phase image reconstructed from the off-axis electron hologram. The electron hologram was taken with external magnetic field 11.7 mT. The skyrmionic bubbles are induced by rapidly changing magnetic field from 1000 mT to 11.7 mT. Based on the in-plane spin rotation sense, the topological charge of skyrmionic bubble is determined as ±1.